There are 12 NRICH Mathematical resources connected to Proof by contradiction, you may find related items under Thinking Mathematically.
Broad Topics > Thinking Mathematically > Proof by contradiction
Eyes Down
Age 16 to 18
Challenge Level
The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?
Mastering Mathematics: the Challenge of Generalising and Proof
Age 5 to 11
This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.
An Introduction to Proof by Contradiction
Age 14 to 18
An introduction to proof by contradiction, a powerful method of mathematical proof.
The Dangerous Ratio
Age 11 to 14
This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
Rational Round
Age 16 to 18
Challenge Level
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
Proof Sorter - the Square Root of 2 Is Irrational
Age 16 to 18
Challenge Level
Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
Staircase
Age 16 to 18
Challenge Level
Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?
Tetra Inequalities
Age 16 to 18
Challenge Level
Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.
Proximity
Age 14 to 16
Challenge Level
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Be Reasonable
Age 16 to 18
Challenge Level
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
NRICH is part of the family of activities in the Millennium Mathematics Project.